Multiscale deformation analysis by Cauchy-Navier wavelets. (English) Zbl 1075.74010

Abeyratne, M. K.; Freeden, W.; Mayer, C.

J. Appl. Math. 2003, No. 12, 605-645 (2003).

Summary: A geoscientifically relevant wavelet approach is established for the classical (inner) displacement problem corresponding to a regular surface (such as sphere, ellipsoid, and actual earth surface). Basic tools are the limit and jump relations of (linear) elastostatics. Scaling functions and wavelets are formulated within the framework of the vectorial Cauchy-Navier equation. Based on appropriate numerical integration rules, a pyramid scheme is developed providing fast wavelet transform. Finally, multiscale deformation analysis is investigated numerically for the case of a spherical boundary.

MSC:

74B05	Classical linear elasticity
74S25	Spectral and related methods applied to problems in solid mechanics
65T60	Numerical methods for wavelets

Keywords:

fast wavelet transform; linear elastostatics